A two-step procedure for testing partial parameter stability in cointegrated regression models

This article studies the problem of testing partial parameter stability in cointegrated regression models. The existing literature considers a variety of models depending on whether all regression coefficients are allowed to change (pure structural change) or a subset of the coefficients is held fixed (partial structural change). We first show that the limit distributions of the test statistics in the latter case are not invariant to changes in the coefficients not being tested; in fact, they diverge as the sample size increases. To address this issue, we propose a simple two-step procedure to test for partial parameter stability. The first entails the application of a joint test of stability for all coefficients. Upon a rejection, the second conducts a stability test on the subset of coefficients of interest while allowing the other coefficients to change at the estimated breakpoints. Its limit distribution is standard chi-square. The relevant asymptotic theory is provided along with simulations that illustrate the usefulness of the procedure in finite samples. In an application to US money demand, we show how the proposed approach can be fruitfully employed to estimate the welfare cost of inflation.